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A study of fuzzy anti-lambda-ideal convergent triple sequence spaces

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
A class with ambiguous status of its elements by a membership function that assigns to each element a grade in the close interval [0, 1]; Lofti Zadeh introduced this idea into theory as fuzzy sets in the year of 1965. A study of fuzzy anti-normed linear spaces by Kočinac on some topological properties motivated us to work on fuzzy anti-normed triple sequence spaces with respect to ideal by using compact linear operator. Further, we prove some theorems, particularly on convergence and completeness.
Wydawca
Rocznik
Strony
353--358
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Department of Mathematics, University Institute of Sciences, Chandigarh University, Mohali, Punjab-140413, India
autor
  • Department of Mathematics, University Institute of Sciences, Chandigarh University, Mohali, Punjab-140413, India
autor
  • Department of Mathematics, School of Engineering, Presidency University, Bangalore, India
  • Department of Mathematics, University Institute of Sciences, Chandigarh University, Mohali, Punjab-140413, India
Bibliografia
  • [1] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math. 11 (2003), no. 3, 687-705.
  • [2] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc. 86 (1994), no. 5, 429-436.
  • [3] S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Optim. 6 (2015), no. 1, 71-78.
  • [4] A. J. Dutta, A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal. 4 (2013), no. 2, 16-22.
  • [5] A. Esi, On some triple almost lacunary sequence spaces defined by orlicz functions, Res. Rev. Discrete Math. Structures 1 (2014), 16-25.
  • [6] A. Esi and C. M. Necdet, Almost convergence of triple sequences, Glob. J. Math. Anal. 2 (2014), 6-10.
  • [7] A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci. 9 (2015), no. 5, 2529-2534.
  • [8] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
  • [9] C. Felbin, The completion of a fuzzy normed linear space, J. Math. Anal. Appl. 174 (1993), no. 2, 428-440.
  • [10] I. H. Jebril and T. K. Samanta, Fuzzy anti-normed linear space, J. Math. Technol. (2010), 66-77.
  • [11] A. K. Katsaras, Fuzzy topological vector spaces. II, Fuzzy Sets and Systems 12 (1984), no. 2, 143-154.
  • [12] V. A. Khan, I-convergent difference sequence spaces defined by compact operator and sequence of moduli, ICIC Express Lett. 13 (2019), 907-912.
  • [13] V. A. Khan, On I-convergent triple sequence spaces defines by a compact operator and orlicz function, TWMS J. Appl. Eng. Math. 11 (2021), 1022-1022.
  • [14] V. A. Khan and M. I. Idrisi, Some fuzzy anti λ-ideal convergent double sequence spaces, J. Intell. Fuzzy Syst. 38 (2020), 1617-1622.
  • [15] V. A. Khan and N. Khan, I-pre-Cauchy sequences and Orlicz functions, Eng. Sci. Res. 5 (2013), 52-56.
  • [16] V. A. Khan, K. Ebadullah, A. Esi, N. Khan and M. Shafiq, On paranorm Zweier I-convergent sequence spaces, J. Math. 2013 (2013), Article ID 613501.
  • [17] V. A. Khan, M. I. Idrisi and U. Tuba, On ideal convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator, Proyecciones 40 (2021), no. 5, 1227-1247.
  • [18] V. A. Khan and N. Khan, On Zweier I-convergent double sequence spaces, Filomat 30 (2016), no. 12, 3361-3369.
  • [19] L. D. R. Kočinac, Some topological properties of fuzzy antinormed linear spaces, J. Math. 2018 (2018), Article ID 9758415.
  • [20] P. Kostyrko, T. Šalát and W. Wilczyński, I-convergence, Real Anal. Exchange 26 (2000/01), no. 2, 669-685.
  • [21] S. A. Mohiuddine, A. Alotaibi and S. M. Alsulami, Ideal convergence of double sequences in random 2-normed spaces, Adv. Difference Equ. 2012 (2012), Paper No. 149.
  • [22] K. Raj, K. Saini and A. Choudhary, Orlicz lacunary sequence spaces of l-fractional difference operators, J. Appl. Anal. 26 (2020), no. 2, 173-183.
  • [23] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput. 17 (2005), no. 1-2, 475-484.
  • [24] A. Şahiner, M. Gürdal and F. K. Düden, Triple sequences and their statistical convergence, Selçuk J. Appl. Math. 8 (2007), no. 2, 49-55.
  • [25] A. Sahiner and B. C. Tripathy, Some I-related properties of triple sequences, Selçuk J. Appl. Math. 9 (2008), no. 2, 9-18.
  • [26] T. Šalát, B. C. Tripathy and M. Ziman, On some properties of I-convergence, Tatra Mt. Math. Publ. 28 (2004), 279-286.
  • [27] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375.
  • [28] L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fe727fa4-070d-4972-910e-86329cf9f086
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